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Discrete Mathematics and Theoretical Computer Science


When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of Sticky Interventions: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is Ω(ln(OP T ))-hard to approximate and that maximizing conversion subject to a budget is (1 − 1 )-hard to approximate. Optimization heuristics which rely on many objective e-function evaluations may still be practical, particularly in relatively-sparse networks: we prove that the long-term impact of a Seed Set can be evaluated in O(|E|2) operations. For a more descriptive model variant in which some neighbors may be more influential than others, we show that under integer edge weights from {0, 1, 2, ..., k} objective function evaluation requires only O(k|E|2) operations. These operation bounds are based on improvements we give for bounds on time-steps-to-convergence under discrete-time reversible-threshold updates in networks.


Network seeding, Spreading phenomenon, Combinatorial optimization, Convergence








c 2016 by the author(s) Distributed under a Creative Commons Attribution 4.0 International License


Peer reviewed accepted manuscript.

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